Differentiate the following w.r.t. x: √((1 + sin x)/(1 - sinx))

Question

Differentiate the following w.r.t. x: \(\sqrt{\cfrac{1+sin\,\text x}{1-sin\,\text x}}\)

√((1 + sin x)/(1 - sinx))

Answer 1

 \(\sqrt{\cfrac{1+sin\,\text x}{1-sin\,\text x}}\)

√((1 + sin x)/(1 - sinx))

Formulae :

• 1 – sin²x = cos²x

Multiplying numerator and denominator by (1 + sin x),

(1 – sin²x = cos²x)

y = sec x + tan x

Differentiating above equation w.r.t. x,